- #1

joneall

Gold Member

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- TL;DR Summary
- Equation in Srednicki QFT book

I've started reading Srednicki's book on QFT, which was starting well. Then I hit on an equation which I just don't understand at all. Since I don't know what the symbol is called, I can only refer to it by its latex name.

Here's the bit. Srednicki defines the following object:

$$f \overleftrightarrow{\partial_{\mu}}g := f (\partial_{\mu}{g}) - (\partial_{\mu}f ) g $$.

Already, it is not clear to me if the second term is a function of a derivative or a product.

He goes on by deriving

$$i \overleftrightarrow{\partial_{0}} \phi(x) =i \partial_0 \phi(x) + \omega \phi(x) $$

clearly using

$$ \partial_0 \phi = i \omega \phi $$.

I will probably feel like an idiot when someone explains this to me, but I just can't get it. How are those two equations compatible? Does this double-arrow beast have a name?

Here's the bit. Srednicki defines the following object:

$$f \overleftrightarrow{\partial_{\mu}}g := f (\partial_{\mu}{g}) - (\partial_{\mu}f ) g $$.

Already, it is not clear to me if the second term is a function of a derivative or a product.

He goes on by deriving

$$i \overleftrightarrow{\partial_{0}} \phi(x) =i \partial_0 \phi(x) + \omega \phi(x) $$

clearly using

$$ \partial_0 \phi = i \omega \phi $$.

I will probably feel like an idiot when someone explains this to me, but I just can't get it. How are those two equations compatible? Does this double-arrow beast have a name?